Investigation of smoothness conditions on the boundary for the strong linear convexity of a domain

1999 ◽  
Vol 51 (12) ◽  
pp. 1935-1938
Author(s):  
V. L. Mel’nik
Keyword(s):  
Linear Convexity ◽  
Strong Linear Convexity

Poisson Lie Groups and Non-Linear Convexity Theorems

1998 ◽  
Vol 191 (1) ◽  
pp. 153-187 ◽  
Author(s):  
Joachim Hilgert ◽  
Karl-Hermann Neeb
Keyword(s):  
Lie Groups ◽  
Linear Convexity ◽  
Non Linear ◽  
Poisson Lie Groups

scholarly journals ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation

2006 ◽  
Vol 2006 ◽  
pp. 1-9
Author(s):  
Lars Filipsson
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Domain ◽  
Holomorphic Mappings ◽  
Convex Domains ◽  
Linear Convexity ◽  
Infinite Dimensional ◽  
Banach Theorem ◽  
Complex Hyperplane

We investigate the concepts of linear convexity andℂ-convexity in complex Banach spaces. The main result is that anyℂ-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given aℂ-convex domainΩin the Banach spaceXand a pointp∉Ω, there is a complex hyperplane throughpthat does not intersectΩ. We also prove that linearly convex domains are holomorphically convex, and that Kergin interpolation can be performed on holomorphic mappings defined inℂ-convex domains.

scholarly journals Local uniform linear convexity with respect to the Kobayashi distance

2003 ◽  
Vol 2003 (6) ◽  
pp. 367-373 ◽  
Author(s):  
Monika Budzyńska
Keyword(s):  
Convex Domains ◽  
Linear Convexity ◽  
Kobayashi Distance ◽  
Bounded Convex

We introduce the notion of local uniform linear convexity of bounded convex domains with respect to their Kobayashi distances.

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